Theorem simp1r3 1159

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1r3	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ch )

Proof of Theorem simp1r3

Step	Hyp	Ref	Expression
1		simpr3 1069	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	3ad2ant1 1082	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ch )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  lshpkrlem6  34402  atbtwnexOLDN  34733  atbtwnex  34734  3dim3  34755  3atlem5  34773  lplnle  34826  4atlem11  34895  4atexlem7  35361  cdleme22b  35629  stoweidlem60  40277